From Infection Clusters to Metal Clusters: Significance of the Lowest Occupied Molecular Orbital (LOMO)

In this paper, the nature of the lowest-energy electrons is detailed. The orbital occupied by such electrons can be termed the lowest occupied molecular orbital (LOMO). There is a good correspondence between the Hückel method in chemistry and graph theory in mathematics; the molecular orbital, which chemists view as the distribution of an electron with a specific energy, is to mathematicians an algebraic entity, an eigenvector. The mathematical counterpart of LOMO is known as eigenvector centrality, a centrality measure characterizing nodes in networks. It may be instrumental in solving some problems in chemistry, and also it has implications for the challenge facing humanity today. This paper starts with a demonstration of the transmission of infectious disease in social networks, although it is unusual for a chemistry paper but may be a suitable example for understanding what the centrality (LOMO) is all about. The converged distribution of infected patients on the network coincides with the distribution of the LOMO of a molecule that shares the same network structure or topology. This is because the mathematical structures behind graph theory and quantum mechanics are common. Furthermore, the LOMO coefficient can be regarded as a manifestation of the centrality of atoms in an atomic assembly, indicating which atom plays the most important role in the assembly or which one has the greatest influence on the network of these atoms. Therefore, it is proposed that one can predict the binding energy of a metal atom to its cluster based on its LOMO coefficient. A possible improvement of the descriptor using a more sophisticated centrality measure is also discussed.